Topological defects in crystals: A density-wave theory

M RAJ L A K S H M I , H R K R I S H N A M U R T H Y and T V R A M A K R I S H N A N Department of Physics, Indian Institute of Science, Bangalore 560 012, India Abstract. A new approach for describing dislocations and other topological defects in crystals, based on the density wave theory of Ramakrishnan and Yussouff is presented. Quantitative calculations are discussed in brief for the order parameter profiles, the atomic configuration and the free energy of a screw dislocation with Burgers vector b =(a/2, a/2, a/2) in a bcc solid. Our results for the free energy of the dislocation in a crystal "of size R, when expressed as (2bZ/4r¢) In (otR/lb]) where ), is the shear elastic constant, yield, for example, the value ~-~ 185 for sodium at its freezing temperature (371°K). The density distribution in the presence of the dislocation shows that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order parameter theory incorporating thermal effects.